1. military technology based on guns, steel weapons, and horses ( the Incas had never seen any of these things before)

2. infectious diseases endemic in Europe, which the Europeans were already immune to, but which decimated the Incans when introduced by the former to the latter's continent. In 1519, Small pox had been introduced to the continent by another Spanish conquistador, Hernando Cortes, who defeated the Aztecs of Mexico

The disease killed Atahuallpa's father and set off a war of succession among his sons. Atahuallpa won but you'd think there would be some disunity among his people as a result of this. This might have weakened their defences

3. The Incans also had a highly centralised chain of command, which meant that Atahuallpa was viewed as an 'invincible' god. He was revered by his men. So, once he was captured, it effectively paralysed their forces.

Other factors included:

European maritime technology; the centralized political organization of European states ( King Charles I of Spain sanctioned Pizarro's voyage to the New World and probably arranged the finance ) and writing ( the significance of this last point cannot be underestimated. It is crucial to understanding precedence and it's role in development)

Atahuallpa was hanged after a period of captivity ( he also naively gave the Spanish enormous Gold and silver as ransom. He thought this was a temporary occupation. He didn't know that the Europeans had colonisation in mind)

Despite some resistance by the Incans, the Spanish pillaged the land- taking their gold, silver, their women and colonised South America.

The Spanish conquest of the Inca Empire was one of the most important campaigns in the Spanish colonization of the Americas.

It set the precedence for European colonisation of the United States of America, farther North, later on

Tupac Amaru was actually the the last Inca emperor, he was captured and executed in 1572 by Spanish Conquistadors. His Inca stronghold was the last to fall.